Originally Posted by bulldogs116
... I know many campgrounds in our area frown on bringing your own wood, they would rather you buy THEIR wood!!..
No, the reason for this is not always to get your money. Here. in the mideast, it's to help prevent the spread of the Emerald Ash Borer. You might want to get a better understanding of this parasite that's literally trying its best to make ash trees extinct by visiting this website.
Emerald Ash Borer Information
One of the most frequent ways this insect has expanded its range of damage is by people bringing (usually unwittingly) firewood from an infected area.
And while your suggestion is good, be advised that if you decide to take your splitter camping with you, you may encounter campgrounds that prohibit the operation of chain saws and wood splitters. Ohio State Parks even go so far as to prohibit the foraging for wood.